We analyze bribing attacks in distributed ledgers from a game theoretic perspective. In bribing attacks, an adversary offers to maintainers a financial reward, in exchange for instructing them on how to behave, with the goal of attacking the protocol's properties. We consider two types of bribing, depending on how the bribes are awarded: i) guided bribing, where the bribe is given as long as the bribed party behaves as instructed; ii) effective bribing, where bribes are conditional on the attack's success, w.r.t. well-defined metrics. We analyze each type of attack in a game theoretic setting and identify relevant equilibria. In guided bribing, we show that the protocol is not an equilibrium and then describe good equilibria, where the attack is unsuccessful, and a negative one, where all parties are bribed such that the attack succeeds. In effective bribing, we show that both the protocol and the "all bribed" setting are equilibria. Using the identified equilibria, we then compute bounds on the Prices of Stability and Anarchy. Our results indicate that additional mitigations are needed for guided bribing, so our analysis concludes with incentive-based mitigation techniques, namely slashing and dilution. Here, we present two positive results, that both render the protocol an equilibrium and achieve maximal welfare for all parties, and a negative result, wherein an attack becomes more plausible if it severely affects the ledger's token's market price.

翻译：我们从博弈论视角分析了分布式账本中的贿赂攻击。在贿赂攻击中，攻击者向维护者提供经济奖励，以指示其行为方式，进而破坏协议属性。根据贿赂的授予方式，我们考虑两种类型：i) 引导式贿赂——只要受贿方按指示行事即可获得贿赂；ii) 有效贿赂——贿赂的发放取决于攻击是否成功，且需依据明确界定的指标。我们在博弈论框架下分析了每类攻击，并识别出相关均衡。对于引导式贿赂，我们证明协议本身并非均衡状态，进而描述了攻击未成功的良好均衡，以及所有参与方均被贿赂导致攻击成功的负面均衡。对于有效贿赂，我们证明协议状态与“全员受贿”状态均为均衡。基于识别出的均衡，我们计算了稳定代价与无政府代价的边界。结果表明引导式贿赂需要额外缓解措施，因此我们的分析最终提出基于激励的缓解技术，即罚没与稀释。在此，我们给出两项积极结果——两者均使协议成为均衡并实现所有参与方福利最大化，以及一项消极结果——若攻击严重冲击账本代币的市场价格，攻击将更易达成。